Question

Write the first five terms of each of the sequences in Exercises 11 to 13 and obtain the corresponding series: a1 = a2 = 2, an = an-1 -1, n > 2.

Answer 1

a1 = a2 = 2, an = an-1 -1, n > 2

⇒ a3 = a2 - 1 = 2 - 1 = 1

a4 = a3 - 1 = 1-1 = 0

a5 = a4 - 1 = 0 - 1 = -1 Hence, the first five terms of the sequence are 2, 2, 1, 0, and –1.

The corresponding series is 2 + 2 + 1 + 0 + (–1) + …